Intersecting spherical pressure tank



1944. J. o. JACKSON ET AL 2,341,044

INTERSECTING SPHERICAL PRESSURE TANKS Filed July 28, 1941 s Sheets-Sheet 1 'II/II/ILIIIIIIIIIII a418 ATTORNEYS.

Feb. 8, 1944- J. o. JACKSON ET AL. 2,341,044

INTERSECTING SPHERIQA/L PRESSURE TANKS 5 Sheets-Sheet 2 Filed Ju] .y 28, 1941 INVENTORS 01. M 9 JKMA'ITORNEYS 1944- J. o. JACKSON ETAL v 2,341,044

INTERSECTING SIHERICAL PRESSURE TANKS 7 Filed July 28, 1941 5 SheetS Sheet 5 11%|: im ATTORNEYS 1944- J. o. JACKSON ET AL INTERSECTING SPHERICA L PRESSURE TANKS Filed July 28. 1941 5 Sheets-Sheet 4 2 filVENT R5 1 BY s8 M 9m W WA. ATTORNEYS Feb. 8, 1944. J. o. JACKSON ETVAL I INTERSEC'IING SPHERICAL PRESSURE TANKS Fil ed July 28, 1941 5 sheets-sheet 5 11f "A, ATTORNEYS to our present invention;

Patented Feb. s, 1944 UNITED STATES PATENT OFFICE lNTERsEcTmGgrPaflnlklucAL li'RESSURE James 0. Jackson, Grafton, and Courtney L.

Stone, Pittsburgh, Pa assignors to Pittsburgh- Des Moines Company, a corporation of Pennsylvania Application July 28, 1941, Serial No. 404,434 9 Claims. (01. 220-3) This invention relates to v containers for the sErage of liquids or gases under pressure.

Several forms of containers for this purpose are now available including cylindrical-containhas been considered to be the only one that is truly stable elastically, that is, it does not tend to change its symmetry with an increase of internal pressure. The sphere is commonly known to have a minimum of surface for any given volume or content and to require a minimum wall thick-' ness and, therefore, a minimum of weight for the storage of any actual volume of gas compressed to any specified pressure. Moreover, a spherical container is commonly regarded as being the only shape of vessel which has these characteristics.

One of the objects of the present invention is to provide a new. composite container for fluids ,producing a container having a .plurality of spherical segmental portions each'of which is bounded on at least one side by a diaphragm-like partition to form a plurality of separatedcompartments and means for equalizing the pressure in such compartments.

Other and further objects and advantages reside in the various combinations, subcombinations. and details hereinafter described and claimedand in such other and further matters as will be understood by those skilled in this art or apparent or pointed out hereinafter.

In the accompanying drawings, in which like numerals designate corresponding parts throughout the various views:

Fig. 1 is a view in elevation of a. tank responding to our invention with parts broken away to show the structure thereof; of a tank responding Fig. 2 illustrates a horizontal-medial section through one of the partial spheres of Fig. land is provided with geometrical indicia by means of which certain calculations can be made relative to a container of this form; k

Figs. 3 and 4 designate in elevation a spherical segment: and a spherical zone whichzare useful in connection with the mathematical aspects of our invention;

Fig. 5 is an elevational view of a modified form of'the invention and showing the supports and piping therefor;

Fig. 6 is a plan view of a composite tank constituting a further modification of our invention and in which the spherical segments are arranged in the general form of a torus;

Fig. 7 is in part an elevational view and in part a sectional view taken on line VII-VII of Fig. 6 and in the direction'of the arrows thereof;

Fig. 8 is a view similar to Fig. 6 but of a further modified form of the invention;

Fig. 9 is a view partly-in elevation and partly in section taken along the line IX-IX of Fig. 8 and in the direction of the arrows thereof;

Fig. 10 is a view similar to Fig. 8 but of a still further modified form of the invention; and

Fig. 11 is a view similar to Fig. 9 but taken along the line XI-XI of Fig. 10 and in the direction of the arrows thereof.

Referring first to the structural features of our new containers, the simplest form thereof is shown in Fig. 1. In that figure the numerals 20 and 2| designate two partial spheres or spherical shell sections which are joined to a common disc oiplate-like member 22 by means of th continuous welds 23. In this form of tank there are two compartments or storage chambers 24 which are separated from one another by means of the diaphragm 22. It is-to be understood that the welds 23 are fluid-tight. As will be more fully understood from what follows, the container of Fig. 1 is usually provided with inlet and outlet pipes which make it possible to cause the chambers 24 to communicate with one another, thus,

..communication with one another. This automatically equalizes the pressure at all times."

In the modified form of container illustrated ,in Fig. 5, it will be noted that there are two, v like end spherical portions 20' and a number of intermediateportions 20" which in this case are in the form of spherical zones. In. other words, end members 20' are incomplete spherical shells. to the extent that the same have a portion thereof removed ,so as to intersect the portions 20" in the manner illustrated, the members 20" being, in effect, the central portions 'of spheres with the diametrically opposite segments removed. A plurality of diaphragms 22' separates the interiorsof members 20' and 20" and, while not visible in Fig. 5. it will be understoodthat the circular welds 2 3 of Fig. l are employed. Thus, the container of Fig: 5 has a plurality or separated compartments or chamof material into the container and for removal of material therefrom, this being effected by suitable valves and by-passes, as will be appreciated by those familiar with piping arrangements.

The fact that all the container portions are thus connected into a common conduit serves to equalize the pressure of the various container portions and twinsure that material supplied to the container portions is stored at the same pressure in all of the various spherical'portions. A suitable relief valve 33 is provided as shown in order to prevent the pressure in the sy tem from exceeding a predetermined maximum. Supports 3'4 are shown as provided at each end of the container and, in general, it is to be understood that we may support the container in any suitable manner which per se forms no part of or restriction upon our present invention. The container need not, however, be elevated.

In Figs. 6 and 7 a further modified form of container has been illustrated and which has the general configuration of a torus. This container .is made up of a plurality of spherical segmental portions arranged in ring form with a hollow center and in which each spherical container portion 20a is bounded by and has secured thereto a pair of diaphragms 22a which converge radially inwardly, thus producing a spherical container portion which has the general configuration of a truncated sector. Each diaphragm 22a is to be understood as being secured in place in the same manner as the diaphragm 22 previously described. The plurality of separated compartments or chambers thus provided in this form of the invention are provided with means for equalizing the pressure in each such either by a piping system of the character of Fig. or by providing one or more apertures in each diaphragm. This particular form of container is especially useful for the storage of liquids under pressure where it is an. vantageous to have acontainer with a diameter .which is large as compared to its height. In

this arrangement also pumping costs are reduced.

The still further modified form of container of Figs. 8 and 9 is, in general, similar to that of Figs. 6 and 7. There are, however, at least two notable distinctions. In the first place, the diaphragms 22b bounding the spherical container portions 20b are all interconnected and merge into a polygonal central diaphragm 22b which is, so to speak, inscribed in the center of the torus and in which is the additional spherical container 2lb. As will be noted from Fig. 9, the container compartments or chambers thus formed arev in communication with each other by means of theopenings 26 provided in the diaphragms 22b and 22b, these openings being reinforced by means of the apertured washerlike elements 25 which are secured to the dia phragms; This form of container is also provided with a piping system like that described in connection with Fig. 5. Under these conditions the piping system may be used solely for charging and discharging the container portions and the matter of pressure equalization is taken care of independently by the apertures 2i aforesaid. The virtue of this form of container is that it is capable of storing large volumes of liquids or gases under pressure and has unusual efiiciency in that all the space occupied by the container is usefully employed. Supporting means such as the braces or columns 21 may be provided and a relief valve 33 prevents excessive pressure condition within the container.

- The modified container of Figs. 10 and 11 is substantially the same as that of Figs. 8 and 9 except mainly for the arrangement and disposition of the diaphragms 220 which are arranged to cross each other at right angles and in such manner as to, in effect, form a plurality'of containers of the type of Fig. 5. The nature of of "P" pounds per square inch greater than the atmospheric pressure exerted on the outside surface of the sphere. In this case if the shell of the sphere is very thin as compared with its radius the said shell will be stressed substantially in tension due to the internal pressure, such teninherent symmetry of the sphere and such tension being numerically equal to PR/2, where P is the sphere. square inch and R in inches the tensional stress T will be expressedin pounds per lineal inch of circumference at the center of the shell thickness at any point on the sphere.

Let it be further assumed that the spherical shell 20 is cut by a plane (BCE) and that the larger portion of the-sphere ABCEA is closed by means of a flat circular diaphragm 22 attached to the said portion of the sphere as, for example, by welding around the circle of intersection as shown at 23. Plane BCE will intersect the spherical shell in the form of a. circle. Now referring to the complete spherical shell it is known that such spherical shell has at all points around the circle caused by the intersection of the said plane a tensile stress equal as previously shown to PR/2. This stress has been indicated on Fig. 2 as T acting upward and to the left and is exactly 65 balanced and counteracted by a like but opposite force T1 acting downward and to the right of the intersecting plane. These forces T and T1 are.

andT5 acting radially inwardly toward central urface BDE is removed it is apparent that strucint C. Now when the portion of the spherical e having the ability to resist forces '1: and '1':

must be substituted in order to maintain equilibrium conditions. If X is assumed to be the angle subtended by the radius BC of the said in- 7 tersecting plane to the center of the sphere 0 assumed that the sphere contains a gas Pressure sion being equal in all directions because of thethe internal gas pressure and R is the radius of If P is expressed in pounds per it is apparent that the angle between the force T and its component Ta'will also be X. The mag-.

nitude of force Ta is, therefore T cos X. The diaphragm I2 is, accordingly, stressed by a force having the magnitude of T cos X acting radially away from the center of the circular diaphragm and its thickness must necessarily be sumcient to resist such force. If the thickness of diaphragm I2 is assumed to be suiflcient to resist such force, it is apparent that the structure ABCEA will be out of equilibrium by the sum of the horizontal forces T: around the circumfel'ence of the diaphragm. Now if .the said structure ABCEA including the portion of the sphere and the circular diaphragm is placed in contact with another exactly similar structure placing the two diaphragms together and fastening them oause the horizontal forces T2 will be exactly offset by similar horizontal forces equal to T4. from the adjoining sphericalsegment and each diaphragm will adequately resist the radial forces T cos X.

One important feature 'of our invention is based on the fact that if two or more spheres of the same or of different sizes are attached together in the manner we have described the weight of the material required in the shell plus the weight of the material required for the diaphragm for each of the spherical portions divided by the volume or contents of each of the spherical portions will be approximately the same as the weight of the material required to form the shell of any of the entire spherical shells divided by their volume. This can be demonstrated by showing that in Fig. 2 the ratio of .the weight per unit of volume of the segment including its circular diaphragm to the volume of that segment is identical with the ratio of the weight of the material of the entire sphere to its volume.

Using the following nomenclature in the English system of units:

Vs is the volume of a sphere or spherical container.

R is the radius of that sphere or spherical element in inches.

P is the pressure in pounds per square inch.

S is the allowable unit working stress in pounds per square inch.

ts is the spherical shell thickness in inches.

i is the diaphragm thickness in inches.

As is the area of the spherical surface.

Ad. is the area of the diaphragm.

w is the weight of the membrane material in pounds per cubic inch.

We is the weight of the spherical shell or spherical element.

We is the weight of diaphragm.

WT is the total combined weight of the shell and diaphragm.

- N is any number of spheres or spherical elements.

X is the angle formed between the axis of the' section.

T is the stressper lineal inch in the spherical membrane. Ta is the stress in diaphragm in a radial direction. An is the area of a circular ring as contrasted with a diaphragm. W3 is the weight of such circular ring.

The following fundamental equations for the solution of the geometry of spheres and spherical elements will be used. Spherical segment 'Volume=V,= (1 1rb(3a"+3c +4b Complete sphere It has been stated that the weight-volume ratio for any number of spheres is the same as though they were combined in one single sphere and also that the same remains true for spherical elements; We will first prove and derive the -constant for a complete sphere and then prove that any portion of a sphere may be removed and the structure closed by the use of a disk member forming part of our invention without changing the weight-volume ratio.

Let it be assumed that the problem is to store a certain volume V of gas under a given pressure of P pounds per square inch, and further let it be assumed that the gas is to be contained in one sphere or N spheres, whichever combination gives the least weight for the desired volume.

.weight of one sphere Now the stress per lineal inch is and the thickness required to withstand this stress is equal to the stress per lineal inch divided by the allowable working stress in pounds per square inch or 5 T PR Substituting Equation 5 in Equation 3 we have.

as an expression for the weight We equal to the following:

. PR 6. W,=A.( )w

and substituting Equation 2 for A; in Equation 6 we have weight of one sphere and for the total weight of N spheres s. W,= 'i yv Now from Equation 1 '9. ram- 4 2,841,044 4 and substituting this value of R for R in Equa-' The area of the disk is equal to a circular area tion 8 we have for the weight of N spheres of which BC is the radius or but which reduces to BC=OB m x a X 1.5 PwV 80 that l1, WT=T Ad=wR Sill X and expressing Equation 11 in terms of weight but sin-3 x x) per unit volume of gas stored we have or 12 ll l.5 Pw Ari=irR (1-cos X) V S Now the thickness of the spherical shell is equal This equationshows the weight/volume ratio of to the stress per inch divided by the allowable a sphere is independent of the number of spheres, unit stress or that is, one sphere would not weigh more or less T PR than N spheres whose total volume is equal to t,=-

the one sphere.

Now it will be proved that a. portion of a sphere and the thickness q e f the dis i equa may be isolated and that the same ratio holds to the stress per oi elreumference multiplied true. In Fig. 2, as previously described, volume by the length ov which it acts divided y the EABCE is an isolated portion oi the sphere allowable unit stress ip ed by the len th EABDE with a plate-like member or. disk 22 comover which the unit stress i efleetive all in like pleting the inclosure. Now this disk is located units 0! as expressed by at any point C on the AD axis in such a manner 25 B that radial lines from the center of the sphere O i to the outer periphery of the disk makes a constantangle x with the AD axis.

Now'the volume of EABCE is equal to the vol- 1 Pll cos X R sin X ume of the complete sphere minus the volume 28 R sin X of EDBCE and using the fundamental equations or for the geometry of the sphere we have Vs=%1rR -%1rb" (3R-b) e g' where r Y J and the weight of the disk is equal to the area of the disk multiplied by the thickness and weight per cubic unit all in like units or expressed by but Wa=Astirw X and the total weight of the complete structure so then i8 7 V.=%a-R %a-(RR cos X) (3R-(RR cos x A Collecting all the equations in a group we have: -rR 1-eos X)(3RR+R cos X) v.=''(2'+a cos X-Cos' x 4 f 2. Ar=2irR=(1+cos x) E "Ti' X) M a. Ad=IR'(1-COSX) PR =,R 2-3 cos X+cos'X) ifi PR +%1R'(3 cos X-cosX) 3 X a 6- w|=Artrw=2IR'(1-i-00S X) to!!! ='-g 2+3 cos Xcos X) v. wi=At-ts-w=s1i=(l-eos=x) -tc-w The spherical surface area of the above volume T=WI+Ws is equal to the area ofthe whole sphere minus Now substituting tin Equation 4 for to in Equathe area of the isolated smaller portion or tion 6 we have 2 l l 4.411% 21121 W: (1 HO. X) 2%; w where R. and b have the same values as above or '5 1 Ar=4rR21rR (R-R cos x) V =4'II'R -2'I'R (1-008 X) ,PRI =11? (4-2+2 cos x) I P- (1+eo X)w I and substitu A.= 21R= (1+cos x) 10- flon 7 we 5 f i The weight of the spherical shell is equal to the area multiplied by the thickness by the weight mama-00.: %;L

per cubic unit all in like units or 'PR,

and then from Equation 8 we have 'I' PR3!!! 2s I Now from Equation 1 it is shown that and substituting this value of R for R in the above equation we have (2+3cos X.cos X) which is the same constant as that found in the previous proof. This proves then that if a portion of a spherical shell is removed and the spheres attached to each other regardless of their size or the angle ofattachment provided only that the pressure in all of the spheres is'the same. In actual practice we place one or more small reinforced intercommunicating holes in. each diaphragm so that the pressures will properly equalize or, in some cases, we findit convenient to attach the inlet and outlet piping to all of the spheres which accomplishes the same result.

Referring to Formula 5 t cos X since that'the distance of the center of the disk'from the center of curvature of the spherical shell bears to the radius of the spherical shell.

For two adjoining truncated spherical shells of the same radius, the required thickness of a single disk to give to the container the elastic stability of a single sphere would therefore vary 5 with the radius of the circle of intersection of the two spherical shells. When the radius of the circle of intersection approaches zero,-the thickness approaches two times the thickness of the spherical shell. When the radius of the intersection approaches the radius of the spherical shell the thickness approaches zero. When the radius of the intersection is equal to the square root of .75 or about .86603 times the diameter of the spherical shell, the thickness of the disk 15 would be the same as that of the spherical shell. If a circular ring were used to reinforce the spherical shell at the circle of intersection instead of our solid diaphragm it may be designed to adequately resist the force T cos X indicated as Tsin Fig. 2. In this type of construction, which is not new, it can be proved that the ring if designed to resist the forces T: transmitted to it from each of the spherical segments, will weigh twice as much as the diaphragm which is the basis of our invention. Further the ring would, in the cases of some forms of our invention, interfere with other essential members. Following is a demonstrationof the fact that the ring will weigh approximately twice that'of a flat circular diaphragm which will withstand the same radial loading.-

Assume two spheres I ii and H as in Fig. 1 except Joined together and reinforced by a circular ring in lieuof a diaphragm. Now from our previous solutions we knowthat -the radial stress per inch of circumference from one sphere is r3= (PR/2) cos X but since we have two spheres T3 becomes and if As. is used to designate the cross-sectional area of the ring we have Now if it be assumed that the center of gravity of the ring is on the theoretical intersecting point of the two spheres then the weight of the ring is equal to the volume generated as the cross section moves along the circumference of a circle passing through the center of gravity of the ring, the said circle having a radius equal to the perpendicular distance from an axis joining the centers of the two spheres to their common circle of intersection, multiplied by the weight per cubic volume of the ring, or a f =A -21-(R sin X)w (PR cos I-R sin X) sin X),

7o Referring to the weight of a diaphragm we have V I structure.

since there are two spheres the weight of two diaphragms I 3 W 2( gg (l cos X) (cos X) W w(1 cos X) cos X ,and comparing the weight of the ring against that of a diaphragm we see that the weight of a ring is twice as much as that required for a diaphragm for the same loading condition.

One ofthe principal advantages of our invention is that comparatively large structures may be built without requiring much, if any, additional support for the relatively thin sheet metal The circular diap'nragms which a each individual spherical segment maybe very simply supported by a central column and radial girder-like members such as are commonly used in large containers.

From the foregoing, it will be apparent to those skilled in this art that by making assemblies of our truncated sphericalshells and diaphragms, containers may be built to suit certain conditions, particularly as to space limitations, such as the diameter and height. Such assemblies will be much more efficient and much'less costly than a single container having the saine diameter and height. Such single containers will require much more material for their construction than our assemblies. This is especially so in cases where the single containerhas relatively flat upper and lower surfaces and is to take the place of the container of Fig. 6. In many cases, it would be impractical to either design or build a single container where it would not only be possible to design but to build a container embodying our invention.

It is to be understood that the foregoing is presented as illustrative and not as limitative and that we may resort to other and further additions, omissions, substitutions and modifications without departing from the principle or scope hereof. fined by the appended claims.

Having thus described our invention, what we claim as new and desire to secure by Letters Pat'- ent is:

2. A container comprising a series of truncated intersecting spherical shell sections and plate-like reinforcing disk members forming partitions between such shell sections and to which such shell sections are joined at their truncations; each such reinforcing member having a thickness equal to the sum of the thicknesses of the adjoining shells when such thicknesses are each multiplied by the ratio that the distance from the center of such reinforcing member to the center of curvature of each such shell bears to the radius of that shell.

3. A container as defined in claim 2 in which the truncated spherical shell sections are so arranged as to approximate a rectangular structure.

4. A container as defined in claim 2 in which the truncated spherical shell sections are arranged in the form of a toms.

- 5. A container as defined in claim 2 in which a number of the plate-lik reinforcing disk members are arranged in' parallel spaced relation.

6. A container as defined in claim 2 in which a number of the plate-like reinforcing disk members lie in planes radiating from the common center of the containen f ,7. A pressure tank comprising at least two truncated intersecting spherical. shell sections having the same radius and thickness and a platelike disk shell reinforcing member forming a partition between such shell sections and to which 4 such shell sections are welded at their truncations, said reinforcing member having a thickness equal to the thickness of one of such shell sections; such shell sections being attached together and to such reinforcing member at their truncations to form a fiuid tight container; each reinforcing member having a radius at the circle of attachment approximating seven eighths of the The invention is rather that de- 1. A container comprising truncated intersecting spherical shell sections and a plate-like reinforcing disk member which forms a partition between such, shell sections and is welded to the adjacent intersecting edges thereof; such reinforcing member having a thickness equal to the sum of the thicknesses of the adjoining shell sections when such thicknesses are each multiplied by the ratio that the distance from the center of such reinforcing member to the center of curvature of each such shell section bears to th radius of that shell section. v

radius of the spherical shell sections.

8. A pressure container comprising a series of truncated intersecting spherical shell sections having the same radius and thickness, and circular plate-like disk reinforcing members welded to adjoining shell sections at their intersection and forming partitions between such shell sections; each such reinforcing member having a thickness equal to the thickness of one such shell section multiplied by the distance between the centers of curvature of adjacent shell sections (11- vided by the radius of one such shell section.

9. A pressure container comprising a series of truncated intersecting spherical shell'sections and circular plate-like disk members located between and joined to adjacent shell sections at their intersection to form reinforcements for and partitions between such shell sections; the'plate-like member between each two adjacent shell sections of the series having a thickness equal to the thicknesspf one such shell section multiplied by the distance from its center of curvature to the center of such plate-like member divided y the radius of curvature of such shell section, plus the thickness of the other shell section multiplied by the distance from its center of curvature to the center of such plate-like member divided by the radius of curvature of such other shell section.

JAMES O. JACKSON.- COURTNEY L. STONE 

